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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 106, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.106
(Mi sigma783)
 

This article is cited in 25 scientific papers (total in 25 papers)

Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations

Concepción Muriel, Juan Luis Romero

Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain
References:
Abstract: This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of $\lambda$-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the $\lambda$-coverings method. The $\lambda$-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent $\lambda$-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different.
Keywords: nonlocal symmetries; $\lambda$-symmetries; telescopic vector fields; order reductions; differential invariants.
Received: July 9, 2012; in final form December 19, 2012; Published online December 28, 2012
Bibliographic databases:
Document Type: Article
MSC: 34A05; 34A34
Language: English
Citation: Concepción Muriel, Juan Luis Romero, “Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations”, SIGMA, 8 (2012), 106, 21 pp.
Citation in format AMSBIB
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\by Concepci\'on~Muriel, Juan~Luis~Romero
\paper Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations
\jour SIGMA
\yr 2012
\vol 8
\papernumber 106
\totalpages 21
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  • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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